If q, r, and s are consecutive even integers and q < r < s, which of t

Let the possible outcome of the equation be c.

Assuming the three numbers to be (r-2), r & (r+2), and substituting in the equation we get the equation as

8r-r^2 = c

Now multiplying by -1 we get

r^2-8r=-(c)

which becomes

r^2-8r+c=0

The determinant of this quadratic equation is thus:

64-4*c

now we compute the determinant for each of the options. The value of c which does not give a perfect square as the determinant will make the roots irrational and hence is not a valid answer:
a. c=-20 gives D=144 -> Rational roots
b. c=0 gives D=64 -> Rational roots
c. c=8 gives D=32 -> Irrational roots
d. c=12 gives D=16 -> Rational roots
e. c=16 gives D=0 -> Rational roots

Hence 8 cannot be the value of the expression.

Answer is C.